1. Priority Information
This application claims priority from European Patent Application No. 03077461.6, filed Aug. 6, 2003, herein incorporated by reference in its entirety.
2. Field of the Invention
The invention concerns a method of controlling a system or process using a learned feed-forward signal, a control system and a lithographic projection apparatus.
3. Description of the Related Art
The essential steps in the manufacturing process of integrated circuits (ICs) are performed by lithographic machines called wafer scanners or wafer steppers. Important modules of these machines are the wafer and reticle stages. According to current state of the art, a wafer stage is normally a motion system, which positions the silicon wafer with respect to the illumination optics with high precision. As ICs are becoming smaller, the required precision increases proportionally. In order to meet positioning specifications that are currently in the order of nanometers, they require careful design. This is not only the case for the mechanical construction, but also for the design of actuators, electronics, software, measurement and control systems, etc.
In control system design, such specifications could so far be met using basic, well known concepts such as conventional feedback with PID (position plus integral plus derivative control action) controllers and conventional feed-forward based on rigid body acceleration. In the future, these concepts may prove insufficient to achieve the desired tracking performance, for which more advanced designs will be needed. As, in the present case, the control objective is to move an object along a predefined trajectory, the control problem is said to be one of “tracking”. The “tracking performance,” as understood in the art, is the accuracy with which the predefined trajectory is followed.
There are different kinds of disturbance acting on the system, including disturbances introduced by the setpoint. That is, although a setpoint is known and deliberate, it will be appreciated that it, nevertheless, “disturbs” the steady state condition. Feedback and feed-forward control deal with the stability and performance (in terms of tracking error), but additional control techniques, for example, iterative learning control (ILC), provides options for significantly improving the tracking performance (compared to conventional feedback and feed-forward) of the processes or systems that execute the same trajectory, motion or operation repetitively.
When only conventional feedback and feed-forward are applied to the considered motion system, the servo error often appears to temporarily exceed the required specifications and, in most cases, it bounds on the allowed amplitude of tracking errors. It then takes a certain settling time for this error to settle within specifications again. Learned feed-forward control can improve the tracking performance and shorten the settling time. For motion systems that repeatedly perform the same movement, a feed-forward technique called Iterative Learning Control or ILC can be applied to improve system performance in terms of elimination of the repeating portion in the tracking error. For a detailed description of iterative learning control, reference is made to Tomizuka M., T. C. Tsao and K. K. Chen “Discrete domain analysis and synthesis of repetitive controllers” Proc. 1988, American Control Conference, June 1988, pp. 860–866.
ILC generates a learned feed-forward signal, effective for providing good tracking control performance. The basic principle behind ILC is that it exploits possibilities to incorporate past repetitive control information, such as tracking errors and control input signals into the synthesis of a new feed-forward signal. Past control information is stored and then used in the control action in order to ensure that the system meets the control specifications such as convergence of the servo error during the learning process. The final result after applying ILC is that the magnitude of the servo errors is relatively small, the periodic disturbances are suppressed or, in other words, the tracking performance is no longer deteriorated by periodic contributions. Such performance improvement allows for shortening settling times and thereby improving productivity of various processes.